Methods, systems and computer program products for characterizing structures based on interferometric phase data

ABSTRACT

Structure profiles from optical interferometric data can be identified by obtaining a plurality of broadband interferometric optical profiles of a structure as a function of structure depth in an axial direction. Each of the plurality of interferometric optical profiles include a reference signal propagated through a reference path and a sample signal reflected from a sample reflector in the axial direction. An axial position corresponding to at least a portion of the structure is selected. Phase variations of the plurality of interferometric optical profiles are determined at the selected axial position. A physical displacement of the structure is identified based on the phase variations at the selected axial position.

STATEMENT OF GOVERNMENT SUPPORT

This invention was made with Government support under grant number5R24-EB00243 from the National Institutes of Health. The Government hascertain rights to this invention.

RELATED APPLICATIONS

This application claims priority to U.S. Utility application Ser. No.11/337,166 filed Jan. 20, 2006 which claims priority from U.S.Provisional Application Ser. No. 60/645,386 filed Jan. 20, 2005, thedisclosures of which are hereby incorporated by reference in itsentirety.

BACKGROUND OF THE INVENTION

The present invention relates to methods and systems for imaging, andmore particularly, to interferometric structure imaging andcharacterization.

Since its introduction in the early 1990's, optical coherence tomography(OCT) has emerged as a promising imaging modality for micrometer-scalenoninvasive imaging in biological and biomedical applications. Itsrelatively low cost and real-time, in vivo capabilities have fueled theinvestigation of this technique for applications in retinal and anteriorsegment imaging in opthalmology (e.g., to detect retinal pathologies),early cancer detection and staging in the skin, gastrointestinal, andgenitourinary tracts, as well as for ultra-high resolution imaging ofentire animals in embryology and developmental biology. Conventional OCTsystems are essentially range-gated low-coherence interferometers thathave been configured for characterization of the scattering propertiesof biological and other samples. By measuring singly backscattered lightas a function of depth, OCT fills a valuable niche in imaging of tissueultrastructure, and provides subsurface imaging with high spatialresolution (˜1-10 μm) in three dimensions and high sensitivity (>110 dB)in vivo with no contact needed between the probe and the tissue. OCT isbased on the one-dimensional technique of optical coherence domainreflectometry (OCDR), also called optical low-coherence reflectometry(OLCR). See Youngquist, R. C., S. Carr, and D. E. N. Davies, OpticalCoherence Domain Reflectometry: A New Optical Evaluation Technique. Opt.Lett., 1987. 12: p. 158; Takada, K., et al., New measurement system forfault location in optical waveguide devices based on an interferometrictechnique. Applied Optics, 1987. 26(9): p. 1603-1606; and Danielson, B.L. and C. D. Whittenberg, Guided-wave Reflectometry with MicrometerResolution. Applied Optics, 1987. 26(14): p. 2836-2842. In someinstances of time-domain OCT, depth in the sample is gated by lowcoherence interferometry. The sample is placed in the sample arm of aMichelson interferometer, and a scanning optical delay line is locatedin the reference arm.

The time-domain approach used in conventional OCT has been used insupporting biological and medical applications. An alternate approachinvolves acquiring as a function of optical wavenumber theinterferometric signal generated by mixing sample light with referencelight at a fixed group delay. Two methods have been developed whichemploy this Fourier domain (FD) approach. The first is generallyreferred to as Spectral-domain OCT (SD-OCT). SD-OCT uses a broadbandlight source and achieves spectral discrimination with a dispersivespectrometer in the detector arm. The second is generally referred to asswept-source OCT (SS-OCT). SS-OCT time-encodes wavenumber by rapidlytuning a narrowband source through a broad optical bandwidth. Both ofthese techniques can provide improvements in SNR of up to 15-20 dB whencompared to time-domain OCT, because SD-OCT and SS-OCT capture thecomplex reflectivity profile (the magnitude of which is generallyreferred to as the “A-scan” data or depth-resolved sample reflectivityprofile) in parallel. This is in contrast to time-domain OCT, wheredestructive interference is employed to isolate the interferometricsignal from only one depth at a time as the reference delay is scanned.

However, the resolution of current OCT techniques is generally limitedby the coherence length of the illumination source. Therefore, currentOCT techniques may not be able to resolve structures of less than ˜1-10μm. For example, the characteristics and dynamics of the cellularsurface may be of interest in many areas of quantitative biology.However, there are few scientific tools which are capable ofnoninvasively acquiring quantitative information about cell surfaceprofiles, displacements, and motions on the nanometer scale.

Dramatic improvements in spatial resolution in optical microscopy haveresulted from the development of confocal, multiphoton, standing waveinterferometric, fluorescence depletion, and point-spreadfunction-engineered apodization techniques, among others. However, someof these techniques which operate noninvasively in the optical far fieldhave so far been limited to spatial resolutions of about λ/10 or on theorder of 50 nm. Substantially better resolution is routinely acquiredwith scanning probe microscopies, including atomic force microscopy(AFM), scanning tunneling microscopy (STM), and scanning near-fieldoptical microscopy (SNOM). These techniques are the diagnosticworkhorses of modern nanoscience and nanotechnology, however theirinnate contact or near-contact operation is by definition invasive tothe surface structure under examination. This invasiveness can take theform of mechanical disruption of the surface structures of interest, oralternatively interfering with or blocking the interaction of surfacestructures with their environment.

SUMMARY OF EMBODIMENTS OF THE INVENTION

According to embodiments of the present invention, structure profilesfrom optical interferometric data can be identified by obtaining aplurality of broadband interferometric optical profiles of a structureas a function of structure depth in an axial direction. Each of theplurality of interferometric optical profiles include a reference signalpropagated through a reference path and a sample signal reflected from asample reflector in the axial direction. An axial position correspondingto at least a portion of the structure is selected. Phase variations ofthe plurality of interferometric optical profiles are determined at theselected axial position. A physical displacement of the structure isidentified based on the phase variations at the selected axial position.

According to some embodiments of the present invention, a system foridentifying structure profiles from optical interferometric dataincludes an interferometer configured to acquire a plurality ofbroadband interferometric profiles of a structure as a function ofstructure depth in an axial direction. Each of the plurality ofinterferometric optical profiles include a reference signal propagatedthrough a reference path and a sample signal reflected from a samplereflector in the axial direction. A signal analyzer is configured toselect an axial position corresponding to at least a portion of thestructure, to determine phase variations of the plurality ofinterferometric optical profiles at the selected axial position, and toidentify a physical displacement of the structure based on the phasevariations at the selected axial position.

While the invention has been described above primarily with respect tothe various method and system aspects of the invention, computer programproducts are also provided.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flowchart illustrating operations according to embodimentsof the present invention.

FIG. 2 is a schematic diagram of optical systems and methods accordingto embodiments of the present invention including a broadband source anda spectrometer.

FIG. 3 is a schematic diagram of optical systems according to furtherembodiments of the present invention including a swept source and aphotodetector array.

FIGS. 4A-4B are schematic diagrams illustrating temporal profile of asample structure (FIG. 4A) and spatial profiling of a sample structure(FIG. 4B) according to embodiments of the present invention.

FIGS. 5A-5F are graphs illustrating temporal profiling of a samplehaving a cell on a glass cover slip according to embodiments of thepresent invention. FIG. 5A is an A-Scan (or magnitude of the complexreflectivity profile of the sample). FIG. 5B is the magnitude of thepositive frequencies of the complex reflectivity profile plotted ingray-scale as a function of time. FIG. 5C is the phase of the positivefrequencies of the complex reflectivity profile as a function of time.FIG. 5D is the phase difference between the scans at a pixel depthcorresponding to the surface of the cell. FIGS. 5E and 5F are the phasedifferences between the scans at a pixel depth corresponding to the topand bottom of the cover slip, respectively.

FIG. 6A is a photomicrograph of an isolated ventricular cardiomyocytefrom a 2-day old chick embryo. FIG. 6B is a graph of the change inoptical path length in microns as a function of time at a position P inFIG. 6A.

FIGS. 7A-7F are graphs illustrating data processing techniques accordingto embodiments of the present invention. FIG. 7A is a graph of athree-dimensional data cube of a reflected interference signal in twolateral dimensions. FIG. 7B is a graph of a selected spectrum from thedata of FIG. 7A. FIG. 7C is a graph of the spectrum of FIG. 7Bre-sampled in wavenumber. FIG. 7D is a graph of re-sampled data that hasbeen Fouier transformed to generate a complex reflectivity profilehaving an amplitude and phase. FIG. 7E is a graph of a three-dimensionaldata cube that illustrates the interferometric phase of each spectrum asshown in FIG. 7D converted to axial distance. FIG. 7F is a graph oftwo-dimensional nanoscale resolution axial distance profile extractedfrom the data block of FIG. 7E.

FIG. 8A is a schematic diagraph of an optical system for measuring anindex of refraction of a sample. FIG. 8B is an enlarged view of thesample of FIG. 8A.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

The present invention now will be described hereinafter with referenceto the accompanying drawings and examples, in which embodiments of theinvention are shown. This invention may, however, be embodied in manydifferent forms and should not be construed as limited to theembodiments set forth herein. Rather, these embodiments are provided sothat this disclosure will be thorough and complete, and will fullyconvey the scope of the invention to those skilled in the art.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the invention. Asused herein, the singular forms “a”, “an” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises”and/or “comprising,” when used in this specification, specify thepresence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of oneor more other features, integers, steps, operations, elements,components, and/or groups thereof.

It will be understood that, although the terms first, second, etc. maybe used herein to describe various elements, components, regions, layersand/or sections, these elements, components, regions, layers and/orsections should not be limited by these terms. These terms are only usedto distinguish one element, component, region, layer or section fromanother region, layer or section. Thus, a first element, component,region, layer or section discussed below could be termed a secondelement, component, region, layer or section without departing from theteachings of the present invention.

Unless otherwise defined, all terms (including technical and scientificterms) used herein have the same meaning as commonly understood by oneof ordinary skill in the art to which this invention belongs. It will befurther understood that terms, such as those defined in commonly useddictionaries, should be interpreted as having a meaning that isconsistent with their meaning in the context of the relevant art andwill not be interpreted in an idealized or overly formal sense unlessexpressly so defined herein. It will also be appreciated by those ofskill in the art that references to a structure or feature that isdisposed “adjacent” another feature may have portions that overlap orunderlie the adjacent feature.

The present invention is described below with reference to blockdiagrams and/or flowchart illustrations of methods, apparatus (systems)and/or computer program products according to embodiments of theinvention. It is understood that each block of the block diagrams and/orflowchart illustrations, and combinations of blocks in the blockdiagrams and/or flowchart illustrations, can be implemented by computerprogram instructions. These computer program instructions may beprovided to a processor of a general purpose computer, special purposecomputer (such as interferometer device), and/or other programmable dataprocessing apparatus to produce a machine, such that the instructions,which execute via the processor of the computer and/or otherprogrammable data processing apparatus, create means for implementingthe functions/acts specified in the block diagrams and/or flowchartblock or blocks.

These computer program instructions may also be stored in acomputer-readable memory that can direct a computer or otherprogrammable data processing apparatus to function in a particularmanner, such that the instructions stored in the computer-readablememory produce an article of manufacture including instructions whichimplement the function/act specified in the block diagrams and/orflowchart block or blocks.

The computer program instructions may also be loaded onto a computer orother programmable data processing apparatus to cause a series ofoperational steps to be performed on the computer or other programmableapparatus to produce a computer-implemented process such that theinstructions which execute on the computer or other programmableapparatus provide steps for implementing the functions/acts specified inthe block diagrams and/or flowchart block or blocks.

Accordingly, the present invention may be embodied in hardware and/or insoftware (including firmware, resident software, micro-code, etc.).Furthermore, the present invention may take the form of a computerprogram product on a computer-usable or computer-readable storage mediumhaving computer-usable or computer-readable program code embodied in themedium for use by or in connection with an instruction execution system.In the context of this document, a computer-usable or computer-readablemedium may be any medium that can contain, store, communicate,propagate, or transport the program for use by or in connection with theinstruction execution system, apparatus, or device.

The computer-usable or computer-readable medium may be, for example butnot limited to, an electronic, magnetic, optical, electromagnetic,infrared, or semiconductor system, apparatus, device, or propagationmedium. More specific examples (a non-exhaustive list) of thecomputer-readable medium would include the following: an electricalconnection having one or more wires, a portable computer diskette, arandom access memory (RAM), a read-only memory (ROM), an erasableprogrammable read-only memory (EPROM or Flash memory), an optical fiber,and a portable compact disc read-only memory (CD-ROM) or digital videodisk (DVD-ROM). Note that the computer-usable or computer-readablemedium could even be paper or another suitable medium upon which theprogram is printed, as the program can be electronically captured, via,for instance, optical scanning of the paper or other medium, thencompiled, interpreted, or otherwise processed in a suitable manner, ifnecessary, and then stored in a computer memory.

Embodiments of the invention may be carried out on human subjects fordiagnostic or prognostic purposes, and may be carried out on animalsubjects such as dogs, cats, or mice for veterinary or researchpurposes. Embodiments of the invention may be carried out in vivo or exvivo, for example, on cells or other living or nonliving tissue.

As used herein, “light” refers to optical radiation suitable in theultraviolet, visible or infrared spectra, and includes optical radiationsuitable for low coherence interferometry.

As used herein, “broadband” refers to a spectral bandwidth that isgreater than about 10 nanometers. “Low coherence” refers to a coherencelength of less than about 100 microns. Low coherence or broadbandinterferometric data refers to data obtained with a low coherence orbroadband light source, or interferometric data synthesized by sweepinga narrowband or coherent light source through a broad spectral range.

According to embodiments of the present invention, structure profilescan be identified from optical interferometric data. As shown in FIG. 1,a plurality of interferometric optical profiles of a structure as afunction of structure depth in an axial direction can be obtained (Block100). The axial direction is generally the direction of propagation ofthe incident optical beam. The interferometric optical profiles includean interference signal of a reference signal reflected from a referencereflector and a sample signal reflected from a sample reflector. In someembodiments, the interferometric optical profile is a Fouriertransformed complex reflectivity profile obtained from a broadbandspectral interferogram. An axial position corresponding to at least aportion of the structure can be selected (Block 102). The axial positioncan be selected based on a conventional Optical Coherence Tomography(OCT) scan that can be used to identify the location of a structure ofinterest. Phase variations of the plurality of interferometric opticalprofiles at the selected axial position can be determined (Block 104). Aphysical profile, such as the displacement of the structure, can beidentified based on the phase variations at the selected axial position(Block 106). The plurality of interferometric optical profiles and/orthe phase variations between the optical profiles is referred to hereinas “Spectral Domain Phase Microscopy (SDPM)” data.

The resolution of conventional optical coherence tomography (OCT) isgenerally limited by the coherence length of the illumination source.However, according to embodiments of the present invention, the analysisof phase variations between a plurality of optical interferometricprofiles at a selected position can provide sub-coherence lengthresolution. For example, the physical displacement of the structure canbe determined with a resolution of less than about 100 nanometers. Insome embodiments, the resolution can be determined to within 10nanometers or one nanometer or less.

In some embodiments, the interferometric optical profiles can beobtained within a selected axial position range or region at a givenlateral position over time, and the axial physical displacement (e.g.,movement) of the structure can be determined. In other embodiments, theinterferometric optical profiles can be obtained within the selectedaxial position region as a function of lateral position, and the lateralphysical displacement (e.g., lateral structure variations) can bedetermined. Accordingly, sub-nanometer scale motions and/or profiles maybe obtained. Sub-wavelength phase information can be position-gated fromlow coherence data. White light interferometry (WLI) full-field orscanning techniques can be used to measure structure including thetopography or variations within a sample interior.

The plurality of interferometric optical profiles can be acquired usingan interferometric system, such as the optical system 210 illustrated inFIG. 2. The optical system 210 includes an interferometer assembly 220and a processor 230. The interferometer assembly 220 includes a sampleoptical assembly 240. The interferometer assembly 220 also includes abroadband light source 222 and a spectrometer 224 connected to a fibercoupler 226 by a source optical fiber 228 a and a spectrometer fiber 228b. The fiber coupler 226 has two output optical fibers 228 c and 228 d.The sample optical assembly 240 includes a collimating lens 242, agalvanometer-driven mirror pair for lateral beam scanning θ_(x,y) 243,an objective lens 244, a documentation port 246, a beam splitter 248, aCCD camera 250, a tube lens 252, a microscope objective lens 254, acamera objective lens 256, and a sample 260. The processor 230 includesan interferometer module 232 and a CCD module 236. The processor 230 isconfigured to receive and analyze data from the interferometer assembly220 and the CCD camera 250.

As illustrated, the sample 260 is a biological cell 264 on a glass slideor cover slip 262. In particular embodiments, the physical displacementof the cell structures, such as the surface of the cell 264 can bedetermined. However, other samples may be provided, including living andnon-living samples.

As shown in FIG. 2, light from the broadband source 222 passes throughthe optical fiber 228 a to the optical fiber 228 d via the fiber coupler226. Light from the optical fiber 228 d is collimated by the collimatinglens 242 and passes through the object lens 244 to the documentationport 246 of the sample optical assembly 240. Light travels to the sample260 via the beam splitter 248, the tube lens 252 and the microscopeobjective lens 254. Light that is reflected from the sample 260 is splitby the beam splitter 248 and travels to the CCD camera 250 (via theobjective lens 256) and the interferometer assembly 220 (via the lenses242 and 244, the optical fiber 228 d, the fiber coupler 226 and theoptical fiber 228 b).

In this configuration, the spectrometer 224 and the CCD camera 250receive a broadband light signal that is reflected from the sample 260.The CCD camera 250 uses the light signal to provide an image of thesample 260, for example, using conventional CCD imaging techniques. Thespectrometer 224 measures various wavelengths from the sample 260 toprovide spectral interferometric signals.

As illustrated, the interferometric signal provided by the spectrometer224 is the interference pattern between a reference signal that isreflected from the cover slip 262 and a sample signal that is reflectedfrom the cell(s) 264 in an axial direction. The cover 262 slip may beused as a reference reflection because it is a relatively strongreflection (typically 4% due to the Fresnel reflection from theair-glass index interface), and it is sufficiently separated from thesurface of the cells 264 to avoid phase corruption as discussed below.Phase corruption may occur when multiple reflectors are spaced closertogether than a coherence length. In some embodiments, the surface ofthe cover slip 262 that is opposite the cell 264 is used as a referencereflector, and the surface of the cover slip 262 that is adjacent thecell 264 is coated with an anti-reflection coating to avoid multiplereference reflections. Configurations in which the reference signal andthe sample signal generally share a common pathway may be referred to asa “common path” configuration. A common path configuration may increasethe phase stability of the signals, which can increase structuralresolution. In some embodiments, the common path configuration canresult in a phase stability that is increased by at least a factor oftwo or more. In particular embodiments, the phase stability may beincreased by a factor of ten or more over non-common path techniques.However, it should be understood that other configurations can be used.For example, the optical fiber 228 c may be optically connected to areference reflector to provide the reference signal.

The processor 230 receives data from the interferometer assembly 220 andthe CCD camera 250. The data can be analyzed by the interferometermodule 232 and the CCD module 236, respectively. The interferometermodule 232 includes an interferometer controller 234 a, a phasevariation generator 234 b and an OCT module 234 c. The interferometercontroller 234 a controls the interferometer assembly 220 to obtain thedesired interferometric data from the optical system 210. For example,the controller 234 a can obtain a plurality of interferometric opticalprofiles of the sample 260 as a function of structure depth in the axialdirection. The interferometric optical profiles can be a Fouriertransform complex reflectivity profile of a broadband spectralinterferogram. The phase variation generator 234 b can determine phasevariations of the interferometric optical profiles at a selected axialposition and identify a physical displacement of the structure based onthe phase variations at the selected axial position. In addition, theOCT module 234 c can provide OCT imaging based on the interferometricoptical profiles of the sample 260.

In some embodiments, an OCT image of the sample 260 from the OCT module234 c can be used to select an axial position in the sample 260, and thephase variation generator 234 b can generate phase variations at theselected axial position. For example, a user can select an axialposition corresponding to a structure in the sample 260. In otherembodiments, a plurality of axial positions or all axial positions of adataset can be selected and imaged according to the techniques describedherein. In some embodiments, the CCD module 236 generates an image ofthe sample 260, and the user can select the lateral position based onthe CCD image.

As illustrated, the optical system 210 of FIG. 2 includes a broadbandsource 222 (i.e., to provide a spectral domain interferometer); however,other light sources can be used. For example, a swept sourceinterferometer configuration is illustrated in FIG. 3. An optical system310 in FIG. 3 includes an interferometer assembly 320 and a processor330. The interferometer assembly 320 includes an optical assembly 340and a tunable wavelength source 322. The optical assembly includeslenses 342, 344, and 356, a beamspliter 358, a CCD camera 324 and asample 360. The sample 360 includes a cover slip 362 and cells 364. Asillustrated, the tunable wavelength source 322 is a narrowband sourcethat is rapidly tuned through a broad optical bandwidth to provide aninterferometric signal. It should be understood that any suitabletunable light sources may be used, such as a tunable laser source or abroadband light source with a tunable filter placed between it and thebulk-optic interferometer 324. The CCD camera 324 can be a one- ortwo-dimensional CCD array, and can be used to provide microscopicimaging and/or detection of an interferometric signal. The processor 330and the components thereof corresponds generally to the processor 230 ofFIG. 2.

Although optical systems according to the present invention aredescribed with respect to the optical systems 210 and 310, it should beunderstood that other configurations can be used, including opticalconfigurations suitable for obtaining OCT data. For example, the fibercoupler 226 and optical fiber 228 d can be omitted, and an opticalcirculator can be used to connect the fibers 228 a, 228 b and 228 d,which may provide efficient collection of mixed light returning from thesample 260. In particular, an optical circulator can be configured suchthat light from the broadband source 222 travels through fiber 228 a tofiber 228 d and the sample system 240, and light from the sample system240 passes through fiber 228 d and to fiber 228 b and the spectrometer224.

As shown in FIGS. 4A-4B, the cover slip 262 includes a reference surface262 a for providing a reference reflection, and the cell 264 includes astructure or sample reflector 264 a. A displacement profile of thesample 260 can be obtained as a function of time (δz(t) in FIG. 4A) oras a function of space (δz(x) in FIG. 4B). In FIGS. 4A-4B, Δz is theoptical path length difference between the reference surface 262 a andthe sample reflector 264 a, and may be sufficiently large so as to bedetected using conventional OCT. Without wishing to be bound by theory,the resolution of a structure using conventional OCT is generallylimited by the coherence length of the light used to obtain aninterferogram. The axial position of the sample reflector 264 a as afunction of time δz(t) (FIG. 4A) or as a function of lateral positionδz(x) (FIG. 4B) may be small compared to the coherence length such thatδz(t) and δz(x) may not be effectively resolved using conventional OCT.According to embodiments of the present invention, profiles of thepositions of sample reflectors (such as reflector 264 a) can beconstrued from repeated measurements of the optical phase correspondingto the position of the sample reflector 264 a. These measurements may bephase unwrapped as desired.

As shown in FIG. 4A, repeated phase measurements may be made at a givenlateral (x,y) and axial (Δz) position to provide a displacement profileas a function of time δz(t) of the sample reflector 264 a. As shown inFIG. 4B, repeated phase measurements may be made at a given axialposition (Δz) to provide a spatial displacement profile as a function oflateral spatial dimensions δz(x) by raster scanning either the samplebeam or the sample 264 in one or both lateral dimensions x or y toobtain one- or two-dimensional spatial profiles of the reflector 264 a,respectively.

In some embodiments, focusing optics can be designed and selected todeliver a desired spot size defining the lateral resolution on thesample 264 at the sample reflector 264 a and to deliver a suitablereference reflection from the reference reflector 262 a. Considerationsfor optimizing the amplitude of the reference reflection, given theintensity and noise properties of the light source, may be similar tothose used in other implementations of Fourier-domain OCT.

Although embodiments according to the present invention are describedherein with respect to detecting physical displacements of a structureover time or as a lateral structure profile, it should be understoodthat phase variations between interferometric optical profiles may beused to determine other physical characteristics. For example, phasevariations between interferometric optical profiles can be used tomeasure the index of refraction of a medium or the index of refractionratio at a boundary between two media.

Embodiments according to the present invention will now be describedwith respect to the following non-limiting examples.

Exemplary Calculations

The spectral interferogram signal recorded in all FDOCT systemsgenerally contains both amplitude and phase information about the sampleoptical field relative to the reference field. For example, the spectralinterferogram data contains direct current (DC) components(corresponding to non-interfering light returning from the sample andreference paths), auto-correlation components (corresponding tointerference between different reflectors in the same sample), andcross-correlation components (corresponding to the desired interferencebetween reference and sample paths). Also, SDOCT techniques tend tocollect spectral interferogram data evenly sampled in wavelength ratherthan wavenumber, since grating-based spectrometers disperse lightaccording to wavelength. Various techniques for designing systems toavoid substantial autocorrelation signals and for re-sampling FDOCT dataso that it is evenly sampled in wavenumber (k) are known and will not befurther described.

For an SDOCT system, the DC and cross-correlation components of there-sampled photocurrent i(k) at the spectrometer due to a single samplereflector are described by Eq. (1) (a similar equation describes thephotocurrent signal from an SSOCT system):i(k)∝ρS(k)δkΔt└R_(R)+R_(S)+2√{square root over (R_(R)R_(S))}cos(2nk[Δz+δz])┘.  (1)Here, Δz+δz gives the position of the sample reflector defined by thepath length difference between it and the reference reflector, n is theaverage group index of refraction of the material over the path lengthdifference Δz+δz, ρ is the detector responsivity, S(k) is the sourcepower density function, δk is the spectrometer spectral resolution, Δtis the spectrometer integration time, and R_(R) and R_(S) are thereference and sample reflectivities, respectively. Δz indicates thereflector position to within the axial resolution of the system(determined by the coherence length of the light source used), whereasδz represents sub-resolution departures of position from Δz. The symbolk represents wavenumber, which is inversely proportional to wavelengthaccording to k=2π/λ.

Procedures for signal processing in FDOCT can involve an inverse Fouriertransform of i(k) to give I(z), a one dimensional, depth-resolved,complex-valued reflectivity profile. A signal of interest in FDOCT isthe magnitude of the complex reflectivity profile |I(z)|, which istypically referred to as the “A-scan,” or depth-resolved samplereflectivity profile. This profile has peak values at x=±2nΔz,corresponding to the reflector position. The magnitude and phase of I(z)evaluated at these peaks are:|I(±2nΔz)=(ρ/2e)S(k)Δt√{square root over (R _(R) R _(S))}E(2nΔz),  (2)∠I(±2nΔz)=±j2nk ₀ δz  (3)where E(2nΔz) is the unity-amplitude time-domain coherence envelopefunction, k₀ is the source center wavenumber, and ∠ is the phaseoperator. The presence of mirror-image peaks at both positive andnegative displacements is referred to as the complex conjugate ambiguityartifact in FDOCT.

In order to sub-resolve structure profiles as a function of time and/orlateral dimension, the interferometric phase is obtained at the depth inthe sample corresponding to the structure of interest, i.e. at I(±2nΔz).Phase and displacement are linearly related at the reflectivity peaks,and conversion from one to the other is accomplished using:

$\begin{matrix}{{{\delta\;{z(t)}} = {\frac{1}{2\;{nk}_{0}}\left( {{\angle\;{I\left( {{2\; n\;\Delta\; z},t} \right)}} - {\angle\;{I\left( {{2\; n\;\Delta\; z},t_{o}} \right)}}} \right)}},} & (4)\end{matrix}$in the case of temporal profiling (where t and t₀ are temporallysequential spectral interferogram acquisition times), or

$\begin{matrix}{{{\delta\;{z(x)}} = {\frac{1}{2\;{nk}_{0}}\left( {{\angle\;{I\left( {{2\; n\;\Delta\; z},x} \right)}} - {\angle\;{I\left( {{2\; n\;\Delta\; z},x_{o}} \right)}}} \right)}},} & (5)\end{matrix}$in the case of spatial profiling (where x and x₀ are laterally separatedspectral interferogram acquisition positions). Using these equations,physical displacements of sub-resolution changes in reflector positioncan be tracked as a function of time or lateral dimension over severalcoherence lengths (i.e. the region over which the coherence envelope isabove the noise floor). In some embodiments, δz varies slowly enoughwith respect to (t-t₀) or (x-x₀) to allow for phase unwrapping.

Illustration of this procedure in the case of temporal profiling isillustrated in FIGS. 5A-5F. FIGS. 5B-5F illustrate a sequence ofspectral interferogram acquisitions at a fixed lateral position on acell surface. The sample is a cell on a glass cover slip. A magneticbead is positioned on the cell, and a magnet tip is positioned over thebead to cause movement of the bead and the cell surface (not shown).FIG. 5A is an A-Scan (or magnitude of the complex reflectivity profileof the sample) at the time indicated by the vertical line 5A in FIG. 5B.FIG. 5B is the magnitude of the positive frequencies of the complexreflectivity profile plotted in gray-scale as a function of time. FIG.5C is the phase of the positive frequencies of the complex reflectivityprofile plotted in gray-scale as a function of time. FIG. 5D is thephase difference between the scans at a pixel depth corresponding to thesurface of the cell (illustrated by the position of the horizontal line5D in FIG. 5C). FIGS. 5E and 5F are the phase differences between thescans at a pixel depth corresponding to the top and bottom of the coverslip, respectively (illustrated by the position of the horizontal lines5E and 5F, respectively in FIG. 5C).

From the magnitude or A-scan data of FIG. 5A, it is possible to identifythe reflections corresponding to the bottom surface of the cover slip,the top surface of the cover slip, and the cell surface. The identifiedpixel depth of these structures are used to extract the phase data atthe same depth pixel, and results in plots of the temporal displacementof the bottom surface of the cover slip (FIG. 5F), the top surface ofthe cover slip (FIG. 5E) and the cell surface (FIG. 5D) over theacquisition time of the spectral interferograms. In this case, thebottom and top surfaces of the cover slip remain essentially fixed asshown in FIGS. 5D-5F, while the cell surface moved in response to themovement of the magnetic bead as shown in FIG. 5D.

The resolution of such displacement measurements may be limited by thephase stability of I(z). Phase stability can be increased through theuse of a common path setup as described with respect to FIGS. 2-3, inwhich much of the phase noise is common-mode. In some embodiments, theresolution of the displacement measurements can be reduced by using abroadband source and spectrometer (i.e., SDOCT), in which case there areno moving parts. In contrast, an SSOCT setup can include a tunablesource, which typically includes moving parts. In the limit of stableseparate reference and sample arms, the sensitivity of displacementmeasurements described herein may be a function of the SNR of thesampled reflector. A fundamental lower limit on the displacementsensitivity of δz(t) due to shot noise may be derived by generalizingi(k) to contain an additive, uncorrelated Gaussian white noise term. Forexample, the sensitivity of δz(t) may be an explicit function of thesignal-to-noise ratio (SNR) of the signal from the reflector whosedisplacement is being measured as follows:

$\begin{matrix}{{\delta\; z_{sens}} \approx {\frac{\lambda_{o}}{4\; n\;\pi}{\sqrt{\frac{1}{{SNR}\left( {S,{\Delta\; t},R_{S}} \right)}}.}}} & (6)\end{matrix}$Temporal Profiling of a Glass Cover Slip

One-dimensional temporal profiling using the systems described in FIGS.2-3 (i.e., both SDOCT and SSOCT interferometers) have been performed.The theoretical sensitivity as been derived and verified in measuringdisplacements of a sample reflector. It is noted that both SDOCT andSSOCT approaches were considered because 1) both are suitable fordifferential temporal and spatial profiling and 2) each technique hasits particular advantages (e.g., FDOCT may exhibits exceptional phasestability due to the absence of moving parts, but typically requiresresampling from wavelength to wavenumber space, while an SSOCT signalcan be linearly sampled in wavenumber space). Initial measurements ofthe displacement stability using the top of the cover slip as the samplereflection, recorded as the standard deviation of repeated displacementmeasurements, yielded displacement stability of 53 pm for theFourier-domain implementation and 780 pm for the swept-sourceimplementation.

Temporal Profiling in Living Cells

One-dimensional temporal profiling of displacements in living biologicalcells has been performed using the phase variations between a pluralityof interferometric optical profiles as described herein. The opticalsystem 210 in FIG. 2 was aligned to position the interferometer focus ofthe interferometer assembly 220 coplanar with the microscope's objectplane focus of the CCD camera 250; an aiming beam (635 nm) coupled intothe source fiber (not shown in FIG. 2) permitted visualization of thelocation from which data were collected. The beam was turned off duringthe experiment, but was replaced with a visual marker using videooverlay. The charge-coupled device (CCD) camera 250 was mounted onto asecond documentation port to enabled simultaneous acquisition ofinterferometric data and video light microscopy. The OCT axialresolution (Δz in Eq. 1), set by the coherence length of the lightsource, was measured to be approximately 8.5 um in air. The spectrometerwas a low-cost commercial version (Ocean Optics USB-2000) with aspectral acquisition time of 5 ms and a readout time of 20 ms. Repeatedspectral measurements were acquired at the same position on the sampleas a function of time at the maximum readout rate of the spectrometer.Phase values obtained from a Fast Fourier Transform (FFT) of there-sampled spectral data at the depth position corresponding to thefeature of interest in the sample (i.e., the cell surface) wereacquired, and unwrapped in time. Displacements were calculated as perEq. 4. Timestamps from the video capture and SDPM software were used inpost processing to correlate the SDPM and video information collected.

Isolated ventricular cardiomyocytes from Day 2 chick embryos wereobtained. Cells were plated in dishes with coverglass bottoms that wereanti-reflective coated for an air-water interface and maintained at 37°C. (a permissive temperature for spontaneous beating) through contactwith a heated stage as shown in FIG. 6A. Individual myocytes werevisually located using light microscopy, and the interferometric signalswere recorded from a site near the apparent center of contractilemotion. Video light microscopy revealed regular cell motions attributedto spontaneous contraction in the examined myocytes. Spectral domaintraces (e.g., the phase variations between a plurality ofinterferometric optical profiles) acquired at the cross-sectional depthcorresponding to the cell surface at position P displayed a uniquespiked pattern of displacement as shown in FIG. 6B, which appearedsynchronously with the beating observed on video microscopy.

Although the magnitude of the spikes was most prominent for phase tracesobtained from the cell surface, similar patterns were observed fortraces at discrete depths directly adjacent to this, while still withinthe source coherence length. The magnitude of the optical pathlengthchange for this single cell was roughly 0.6 μm, which is in goodagreement with the magnitude of cell surface motion found inspontaneously contracting myocytes in a previous experiment usingnear-field scanning optical microscopy.

Sub-Resolution Profiling is Depth-Gated Using Broadband Interferometry

By examining the phase variations between a plurality of interferometricoptical profiles to perform structure profiling, broadband (otherwiseknown as low-coherence) interferometry can be employed both to obtainthe interferometric phase information which is the basis of thesub-resolution measurement, as well as to simultaneously gate out allother axially displaced reflections, either from within the sample orfrom elsewhere in the optical system. The resolution of the coherencegate is given by the coherence length of the light source, and just asin conventional optical coherence tomography, this gate is typically afew micrometers in length and is also a very strong discriminatoragainst reflections from outside of the gate. This coherence gate may beused in many sub-resolution profiling applications, and can serve twofunctions. First, the coherence gate rejects spurious reflections fromoptical elements outside of the sample from interfering with the opticalphase measurement. Second, the coherence gate enables the selection of afew micrometers of depth in the sample within which surface profilingusing the phase variations between a plurality of interferometricoptical profiles can be performed.

Depth-Priority Scanning Multidimensional SDPM

As discussed above, nanoscale resolution of depth-gated featureprofilometry in samples as a function of temporal delay (by waiting aset delay time between phase acquisitions), or of lateral position (bylaterally translating either the sample or the optical beam betweenphase acquisitions) can be performed. In both cases, the profilingmeasurement is understood to be obtained in the depth direction (denotedby z in Eqs. 1-5) by processing of spectral interferometric datameasured as a function of wavenumber k (possibly requiring re-samplingfrom wavelength to wavenumber, in the case of SDOCT implementations).Lateral profiling may be extended to scanning in more than one lateraldimension (i.e., both x and y) between phase acquisitions (see FIG. 2),from which data a 2-dimensional surface profile of the structure ofinterest with nanoscale resolution may be constructed. The lateralscanning may be accomplished using, for example, a raster scan pattern,or any other 2D lateral scan pattern which may be optimized to obtainthe data in the order which is optimal for the measurement to beperformed. In these implementations, the spectral data may be acquiredat each lateral position prior to moving on to the next lateralposition, thus this mode of scanning may be referred to asdepth-priority scanning. Other scanning approaches may result in alonger time period for acquisition of the spectral data, and smallmotions of the sample during spectral acquisition may degrade thespectral data thus obtained. If motion of the sample is a concern (as itis likely to be for any living biological sample), the spectraldimension may be acquired rapidly, so that sample motion during spectralacquisition may be less likely to “wash out” the interferometric data.For example, using an SDOCT interferometer set-up (FIG. 2),depth-priority scanning may be accomplished by using a high-speed linecamera in the focal plane of a grating-based spectrometer as ahigh-speed spectrometer. Using the SSOCT interferometer set-up,depth-priority scanning is accomplished by using a rapidly tuned lasersource or alternatively, a rapidly tuned tuning element such as atunable Fabry-Perot cavity placed between a broadband light source andthe interferometer.

To conduct multidimensional structural profiling on living samples suchas cells for which motion is a concern for inducing fringe washout,serial line- or raster-scanning of the spot from an axial profiling,high-speed optical interferometry system may be used as illustrated inFIG. 2. One- and two-dimensional raster-scanning phase microscopy may beused. The spectral acquisition time of such a system may be limited bythe short integration times (down to 30 μs) available from high-speedline-scan cameras utilized in the spectrometer, and the system canremain based on convenient and flexible single mode optical fibers.

Parallel Acquisition Multidimensional Structural Profiling

To accommodate situations where fringe washout is not necessarily aconcern, one or more lateral dimensions may be acquired simultaneouslyusing array detectors. These implementations share the characteristicthat they are bulk-optic systems where at least one dimension of thesample is directly optically imaged onto one dimension of an arraydetector (such as a CCD detector or photodiode array), where it overlapswith reference light.

It should be understood that various light sources and detectors can beused to acquire interferometric data according to embodiments of thepresent invention.

For example, the optical systems 210 and 310 of FIGS. 2 and 3 can beconfigured as a bulk-optic layout to image one lateral dimension ofcombined sample and reference light onto one dimension of an arraydetector, such as a CCD array. In some embodiments, such aninterferometric system is illuminated by one wavelength of light from atunable light source (such as tunable wavelength source 322 of FIG. 3).A one-dimensional lateral image of the sample can be acquired for eachwavelength of the tunable light source by the one-dimensional detector.The light source can then be tuned to a second wavelength to acquire asecond one-dimensional lateral image. The acquisition of a plurality ofsuch one-dimensional images at a sequence of wavelengths results in atwo-dimensional raw dataset including a lateral and a spectraldimension.

As another example, a two-dimensional array detector such as atwo-dimensional CCD array or two-dimensional photodiode array can beused to detect light reflected from the sample. The two-dimensionalarray can be a detector in an imaging spectrometer, such that onelateral dimension of combined sample and reference light is directlyimaged onto one of the dimensions of the two-dimensional array detector,while the combined sample and reference light is spectrally dispersed inthe orthogonal spatial dimension. Accordingly, every acquisition fromthe detector array results in a two-dimensional dataset including alateral and a spectral dimension.

As yet another example, a “full field” optical profile can be obtainedusing a two-dimensional CCD array and a tunable light source. A commonpath bulk-optic interferometer can be used to illuminate the sample anddetect the back-scattered light on a two-dimensional CCD camera. Atwo-dimensional lateral image of the sample can be acquired for eachwavelength of the tunable light source. The light source can then betuned to a second wavelength to acquire a second two-dimensional lateralimage. The acquisition of a plurality of such two-dimensional images ata sequence of wavelengths results in a three-dimensional raw datasetincluding two lateral dimensions and a spectral dimension.

Various data processing techniques are illustrated in FIGS. 7A-7F. Theraw data acquired by each of the alternate embodiments for each phasemeasurement comprises a raw spectral interferogram (containing axialdata) for each lateral point in a one-dimensional or two-dimensionalspatial array (i.e., a spectral dimension by two lateral dimensions).The full three-dimensional dataset may thus be visualized asthree-dimensional data cube, with the axial dimension representingspectrum and the other two dimensions representing lateral displacement(FIG. 7A). As discussed above, in some embodiments, only data in onlyone lateral dimension is acquired. In this case, the data may beconsidered as a two-dimensional vertical slice through the data cube inFIG. 7A in either the x or y direction. Each of the raw spectralinterferograms can be first re-sampled from being unevenly sampled inwavenumber (for example, from being evenly sampled in wavelength as inFIG. 7B) to be evenly sampled in wavenumber, as illustrated in FIG. 7C.Each spectral interferogram is then Fourier transformed into complexreflectivity data having magnitude and phase, as described in Eqs. (2)and (3) and illustrated in FIG. 7D. The phase data is then unwrapped ifnecessary, and may be converted into distance using Eq. 5. The resultingnanoscale distance profiles as a function of one or two lateraldimensions may be expressed as a horizontal slice through thethree-dimensional dataset of FIG. 7E, which has now been transformedinto an axial distance as a function of one or two lateral distances.When only data in only one lateral dimension has been acquired, aone-dimensional nanoscale axial distance profile as a function of onelateral direction as shown in each horizontal or vertical slice of FIG.7E can be calculated. When data in two dimensions has been acquired, atwo-dimensional nanoscale axial distance profile as a function of bothlateral directions, as illustrated in 7E can be calculated.

Reduction of Artifacts from Phase Corruption

The calculation of pathlength displacement from phase in Eqs. (4) and(5) is generally derived under the assumption that pathlength and phaseare generally linearly related. The linearity of this relationshipfollows directly from Fourier transform analysis, however; thisassumption is identically true in the limit that the phase being sampledarises from an isolated reflector. For a band-limited spatial frequencyresponse signal, phase contributions from distant reflectors may benegligible. On the contrary, closely spaced reflectors can degrade theassumed linear relationship between phase and optical pathlength througha process referred to as phase corruption. For example, cells thinnerthan ˜20 μm may suffer from phase corruption when the presence of astrong reflection from the top of the glass coverslip that serves as thereference signal overlaps the reflection from the cell surface, thusadversely influencing the phase values obtained for motion at the cellsurface. (Even if the top surface of the cover slips are anti-reflectioncoated to reduce this effect).

because thinner samples will always arise no matter how short thecoherence length, an inexpensive algorithmic solution may be used. Inaddition to resolving sample from reference features, such a solutionmay also enable imaging of sub-cellular structures that are usuallyambiguously incorporated into neighboring structures due tosource-constrained limits on axial resolution.

The analysis begins by modifying Eq. (1), the interferometric componentof the signal current incident on a single pixel element of a photodiodearray used in conventional SDOCT implementations, to allow for a samplewith N distinct reflectors. In this case, Fourier transformation yieldsa complex quantity I(z) whose phase (prior to unwrapping) at spatialdomain position z is given by:

$\begin{matrix}{{\theta(z)} = {{\tan^{- 1}\left( \frac{\sum\limits_{n = 1}^{N}{A_{n}{\sin\left\lbrack {2\;{k_{0}\left( {z - z_{n}} \right)}} \right\rbrack}{\mathbb{e}}^{\frac{- {({z - z_{n}})}^{2}}{2\; o^{2}}}}}{\sum\limits_{n = 1}^{N}{A_{n}{\cos\left\lbrack {2\;{k_{0}\left( {z - z_{n}} \right)}} \right\rbrack}{\mathbb{e}}^{\frac{- {({z - z_{n}})}^{2}}{2\; o^{2}}}}} \right)}.}} & (7)\end{matrix}$Here, n represents each reflector, A_(n) is the magnitude of thebackscattered signal for a reflector at position z_(n), and thecoherence envelope function is written explicitly as a function of thecoherence length of the light source σ. The effect of reflector n on theobserved phase of reflector n+1 when the two are spaced a distance z₀apart is characterized by the derivative of Eq. 7, which can be writtenas

$\begin{matrix}{{\frac{\partial{\theta\left( z_{n + 1} \right)}}{\partial t} = {k_{0} - \frac{y\; M\;{\sin\left( {k_{0}z_{0}} \right)}}{\sigma^{2}\left( {1 + {M^{2}{\mathbb{e}}^{\frac{z_{0}^{2}}{2\;\sigma^{2}}}} + {2\; M\;{\cos\left( {k_{0}z_{0}} \right)}}} \right)}}},} & (8)\end{matrix}$where M=A_(n+1)/A_(n) is the relative magnitude between the two peaks.In the limit that z₀→∞ (the reflectors are very distant) or M→∞ (thesample is reduced to a single reflector), the slope is identically k₀ atall spatial positions z, and the linear relationship between phase anddisplacement is preserved. Deviation of the slope from this expectedvalue is inevitable when reflectors are too close. As can be seen by Eq.8, there are four primary contributors to phase corruption: k₀ and σ areknown parameters of the light source used; while M and z₀ are parametersinherent to the sample.reflectors are too close. As can be seen by Eq. 8, there are fourprimary contributors to phase corruption: k₀ and σ are known parametersof the light source used; while M and z₀ are parameters inherent to thesample.

A first approach for correcting for the effects of phase corruption isto estimate values of M and z₀ from known properties of the sample, andthen to use Eq. (8) to predict a correction factor for the measureddisplacement data. The separation between the peaks, z₀, corresponds tothe thickness of the sample, which may be known or be readily estimated.For example, for cell samples z₀ may be known a priori (i.e., forstandard cell types) or estimated from independent measurements (i.e.,from other optical interferometric measurements). For industrialsamples, z₀ may be known from manufacturing processes or may be measuredindependently (i.e., from STM or other optical interferometricmeasurements). The relative magnitude between the peaks, M, may beestimated from the Fresnel reflection magnitudes at the top and bottomboundaries of the sample, given the known indices of refraction of thesample material (i.e., cytoplasm) the structure supporting it (i.e., aglass cover slip), and the air above it.

A second approach for correcting phase corruption due to overlappingreflectors involves acquisition and subtraction of a “backgroundspectrum” which includes all reflectors except the reflector ofinterest. For the case of a cell or other sample on a cover slip, forexample, a suitable background spectrum could be acquired from the coverslip in the absence of the sample. To recover the corrupted phase, the“background” spectrum is subtracted from the raw spectrum data beforeprocessing. This subtraction can be done before or after wavelength dataare resampled to be evenly spaced in wavenumber. In this approach, thepower intensity for all the background reflectors in the two datasetsmay be matched; however the power intensity can be adjusted bymultiplying one or more dataset by a constant factor.

A third approach is as follows. Background spectral data as describedabove for the second approach can be reconstructed entirely in software,and then used to correct the corrupted dataset as described above. Thesource spectrum can be recreated and effectively convolved with thepoint spread function of the spurious reflector that is to besubtracted. For a perfect reflector, this amounts to multiplying theFourier transform of the source spectrum by a sinusoid whose frequencymatches that of the spurious reflector location. To recreate the sourcespectrum, a low-pass filtered version of the corrupted dataset can beused to extract the raw spectrum, which appears centered at z=0 in thespatial domain because of the DC signal terms. Alternatively, a prioriknowledge of the source spectrum can be used to generate a replica ofthe source. In both methods, knowledge of the point spread function ofthe reflector may be difficult to ascertain, but in practice theassumption of a perfect reflector may be sufficient.

Noncontact Index of Refraction Measurement

According to embodiments of the present invention, nanoscale opticalpathlength measurement capabilities can be used for noncontact index ofrefraction measurements of a sample. A sample beam of a broadbandinterferometer can be propagated through the sample, and a plurality ofinterferometric optical profiles comprising a reference signalpropagated through a reference path and the sample signal propagatedthrough the sample can be obtained. Phase variations between theplurality of interferometric optical profiles evaluated at the pathlength difference between the sample and reference paths can bedetermined, and variations in an index of refraction of the sample canbe identified based on the phase variations. In particular embodiments,the sample includes two media, each having an index of refraction. Theindex of refraction of the one medium can be calculated based on a knownindex of refraction of the second medium and the identified variationsin the index of refraction of the sample.

For example, a medium within which it is desirable to measure smallchanges in the index of refraction may be placed in the sample arm of anSDOCT or SSOCT interferometer. A plurality of interferometric opticalprofiles of a fixed reflector terminating the sample arm may be obtainedas a function of depth in an axial direction. Phase variations betweenthe plurality of interferometric optical profiles can be determined, andmay be attributed to variations in the index of refraction of the mediumtraversed by the light in the sample arm. As in previous embodiments,the use of a common-path interferometer design can increase the phasestability of the measurement and thus the accuracy with which index ofrefraction variations may be measured.

According to embodiments of the present invention, measurements of smallchanges in the index of refraction of a medium at an optical interfacemay be made. In particular, as shown in FIG. 8A, a broadband lightsource 422 is passed via optical fibers 428 a, 428 b, 428 c and 428 d,fiber coupler 426 and lens 442 onto a sample 460. As shown in FIG. 8B,the sample 460 includes a flowing medium 464 and a prism 462. Reflectedlight is detected by the spectrometer 424. As illustrated, the referencereflection and the sample reflection are both reflected from the sample460, i.e., a “common path” configuration. The medium 464 can be asolution.

In some applications in biomedical and scientific measurements, it maybe desirable to measure changes in the index of refraction of media,such as the flowing medium 464, with high accuracy. For example, asystem which is capable of monitoring small changes in the refractiveindex of a fluid in a flowing tube or a reservoir may have applicationsin noninvasive sensing of analytes and/or impurities, for example forbiochemical analyte sensing in analytical chemistry applications, or forimpurity or toxin detection in municipal water systems. Additionally,this type of system may be used in powerful biosensors in which specificmolecules or compounds (i.e., antibodies or DNA strands) may beimmobilized via chemical means on the dielectric surface, and smallchanges in refractive index result from attachment of complementarymolecules (antigens or complimentary DNA strands) precipitating out ofthe flowing solution. Such a system based on the noninvasive measurementof refractive index may have the advantage of label-free detection ofthe analyte, impurity, or molecule of interest, provided that thecompound effects the refractive index of the fluid in a known way, andthat other confounding effects on the refractive index of the fluid(such as temperature fluctuations or fluctuations in the concentrationsof other impurities) can be accounted for.

Accordingly, the techniques described herein can be used for noninvasivemonitoring of refractive index. At angles larger than the critical anglefor total internal reflection from a planar boundary between dielectricmedia, the phase of the internal reflection coefficient depends upon theratio of the refractive indices (n₁ and n₂ in FIG. 14B) of the media onboth sides of the interface. For the TE and TM polarized waves,respectively,

$\begin{matrix}{{{\tan\left( \frac{\varphi}{2} \right)} = \frac{\sqrt{{\sin^{2}\theta} - {\sin^{2}\theta_{c}}}}{\cos\;\theta}}{and}} & (9) \\{{\tan\left( \frac{\varphi}{2} \right)} = {\frac{\sqrt{{\sin^{2}\theta} - {\sin^{2}\theta_{c}}}}{\cos\;{\theta sin}^{2}\theta_{c}}.}} & (10)\end{matrix}$In these expressions, θ is the internal angle of reflection at theinterface (illustrated in FIG. 8B), θ_(c) is the critical angle fortotal internal reflection (given by=sin⁻¹(n₂/n₁)), and φ is the phase ofthe reflection coefficient. Accordingly, φ corresponds to the phase ofthe complex reflectivity profile obtained by Fourier transformation ofspectral interferogram data according to Eq. (5), evaluated at the axialdepth corresponding to the position of a sample reflector wherein thesample arm path includes at least one total internal reflection at theindex boundary of interest. As illustrated in FIG. 8B, the flowingmedium 464 is in contact with the hypotenuse of a glass prism of knownrefractive index n₁, for example a right angle prism 462. Thecommon-path reference and sample light is incident on the prism 462normal to one of the faces 462 a thereof, and the reflection from theface 462 a is used as the reference reflection for spectralinterferometry (this reflection may be coated to provide a referencereflectivity which optimizes the signal-to-noise ration of theinterferometric measurement). The sample arm light which traverses theface 462 a is substantially internally reflected at the hypotenuse ofthe prism 462, and is incident at normal incidence to the other flatface 462 b. Light retro-reflected from the face 462 b (which mayoptionally be coated to be more efficiently reflected) is used as thesample arm end reflection, and the sample arm light thus re-traces itspath through a second total internal reflection at the hypotenuse face462 c of the prism 462, and re-joins the reference light at the incidentpath. So long as the angle of incidence θ at the hypotenuse reflectionis greater than the critical angle θ_(c), the interface satisfies thecondition for total internal reflection and the phase of the reflectionat that interface will be described by Eqs. (9) and (10) for therespective polarization states. Thus, small changes in the refractiveindex of the fluid outside of the hypotenuse face 462 c of the prism,n₂, can result in measurable changes in the phase of the complexreflectivity profile from Eq. (3), evaluated at the depth positioncorresponding to the sample reflection from the face 462 b of the prism.

As illustrated in FIGS. 8A-8B, which use a right angle prism, the anglewith which the sample reflection is incident on the hypotenuse face 462Cof the prism is 45 degrees, thus the critical angle θ_(c) is less than45 degrees. The angle θ_(c) for an interface between standardborosilicate glass (n₁=1.5) and air (n₂=1.0) satisfies this condition(θ_(c)=41 degrees); thus this system may be used to monitor smallchanges in the index of refraction of air or other gases due toimpurities or other factors. If the fluid has an index of refractionclose to that of water (n₂=1.33), then a right-angle prism with a higherindex of refraction (n₁>1.88) must be used to ensure that θ>θ_(c).

Although FIGS. 8A-8B are illustrated with respect to a flowing medium464 and a prism 462, it should be understood that other configurationscan be used to measure an index of refraction. For example, opticalsetups may be designed to allow for reference and sample reflections tobe obtained for smaller angles of incidence on the index interface ofinterest (i.e., by not using a right-angle prism or by not using thefront and back faces of a right-angle prism for the reference and samplereflections). For example, a transmissive sample arm could be designedwhich executes only a single reflection from the index of refractionboundary, and re-joins the reference light using an optical circulatoror coupler. In addition, alternative optical setups may also be readilydesigned to more closely match the reference and sample optical paths,in case the pathlength through the prism is too great given the spectralresolution of the SDOCT or SSOCT system used to collect and process thespectral interferometric data. In some embodiments, the phase of aninternal reflection may thus be monitored from a refractive interface(either in single or double pass), and small changes in the refractiveindex of the material on the other side of the interface may bemonitored noninvasively.

In some embodiments, the phase difference upon total internal reflectionat a boundary may be substantially increased beyond that indicated inEqs. (9) and (10) by using the principles and techniques of surfaceplasmon resonance (SPR). Common-path phase-shift interferometrytechniques have been used in biosensing systems for measuring phasevariations caused by biomolecular interactions on SPR sensing chipswithout the need for additional labeling. A phase variation which isseveral orders of magnitude more sensitive to external refractive indexvariations that indicated in Eqs. (9) and (10) may be achieved bycoating the refractive interface boundary with a thin film of goldmetal, and adjusting the angle of reflection to the well-characterizedSPR angle. Then, the measurements of phase differences described hereincan be performed.

In the drawings and specification, there have been disclosed typicalpreferred embodiments of the invention and, although specific terms areemployed, they are used in a generic and descriptive sense only and notfor purposes of limitation, the scope of the invention being set forthin the following claims. Moreover, various spectrometer and detectorconfigurations and techniques known to those of skill in the art may beused to accomplish the functions and features of the embodimentsdescribed herein.

1. A method of identifying variations in the index of refraction of asample, the method comprising: propagating a sample beam of a broadbandinterferometer through the sample; obtaining a plurality of broadbandinterferometric complex optical profiles of a portion of the sample as afunction of sample depth in an axial direction, each of the pluraliatyof broadband interferometric complex optical profiles comprising areference signal propagated through a reference path and reflected froma reference reflector and a sample signal propagated through a samplepath to the sample and reflected from a sample reflector, wherein theinterferometric complex optical profiles include magnitude data andphase data as a function of depth; determining phase variations betweenthe phase data of the plurality of interferometric complex opticalprofiles evaluated at the path length difference between the sample andreference paths at a selected axial position; and identifying variationsin an index of refraction of the sample based on the phase variations ofthe phase data at the selected axial position.
 2. The method of claim 1,wherein the sample comprises a first medium having a first index ofrefraction and a second medium having a second index of refraction, themethod further comprising calculating the first index of refraction ofthe first medium based on the second index of refraction of the secondmedium and the identified variations in the index of refraction of thesample.
 3. The method of claim 2, wherein the sample signal is aninternal reflection of the sample beam between the first and secondmedia.
 4. The method of claim 3, wherein a path of the sample beam issubstantially entirely within the second medium and a boundary betweenthe first and second medium.
 5. The method of claim 1, wherein thesample comprises the sample reflector.
 6. The method of claim 1, whereinthe broadband interferometric complex optical profiles are obtainedusing a light source spectrum of at least about 10 nanometers.
 7. Themethod of claim 1, wherein the plurality of complex opticalinterferometric profiles are a complex reflectivity profile obtainedfrom a Fourier or inverse Fourier transform of a broadband spectralinterferogram.
 8. The method of claim 1, wherein the sample comprises aportion of a biological cell.
 9. The method of claim 1, wherein thesample comprising a flowing fluid.
 10. The method of claim 1, whereinthe plurality of complex optical interferometric profiles are acquiredusing an interferometer having a substantially common sample andreference pathway.
 11. The method of claim 1, wherein the plurality ofcomplex optical interferometric profiles are acquired using a SpectralDomain Optical Coherence Tomography (SDOCT) interferometer.
 12. Themethod of claim 1, wherein the plurality of complex opticalinterferometric profiles are acquired using a Swept Source OpticalCoherence Tomography (SSOCT) interferometer.
 13. A system foridentifying variations in an index of refraction of a sample fromoptical interferometric data comprising: an interferometer configured toacquire a plurality of broadband interferometric complex opticalprofiles of a sample as a function of depth in an axial direction, eachof the plurality of interferometric complex optical profiles comprisinga reference signal propagated through a reference path and a samplesignal reflected from a sample reflector in the axial direction, whereinthe complex optical profiles include magnitude data and phase data as afunction of depth; and a signal analyzer configured to select at leastone axial position corresponding to at least a portion of the sample, todetermine phase variations between the phase data of the plurality ofinterferometric complex optical profiles at the selected axial position,and to identify a variation in an index of refraction of the samplebased on the phase variations of the phase data at the selected axialposition.
 14. A computer program product for identifying variations inan index of refraction of a sample from optical interferometric datacomprising: a non-transitory computer readable medium having computerreadable program code embodied therein, the computer readable programcode comprising: computer readable program code configured to obtain aplurality of broadband interferometric complex optical profiles of asample as a function of depth in an axial direction, each of theplurality of interferometric complex optical profiles comprising areference signal propagated through a reference path and a sample signalreflected from a sample reflector in the axial direction, wherein thecomplex optical profiles include magnitude data and phase data as afunction of depth; computer readable program code configured to selectat least one axial position corresponding to at least a portion of thestructure; computer readable program code configured to determine phasevariations between phase data of the plurality of interferometriccomplex optical profiles at the selected axial position; and computerreadable program code configured to identify a variation in an index ofrefraction of the sample based on the phase variations of the phase dataat the selected axial position.